Haelterman et al . also showed that when the Quasi-Newton Least Squares Method is applied to a linear system of size, it converges in at most steps although like all quasi-Newton methods, it may not converge for nonlinear systems.
42.
Haelterman et al . also showed that when the Quasi-Newton Inverse Least Squares Method is applied to a linear system of size, it converges in at most steps although like all quasi-Newton methods, it may not converge for nonlinear systems.
43.
Another approach for solving fluid dynamic equations in a grid free framework is the moving least squares or least squares method ( Belytschko et al . 1996, Dilts 1996, Kuhnert 99, Kuhnert 2000, Tiwari et al . 2001 and 2000 ).
44.
:: If you want to go one step further and draw a straight line that isn't parallel to the axis, you could use a sum of least squares method or some other method to fit a straight line to the date.
45.
This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed : the method of moments, the maximum likelihood method, the least squares method and the more recent method of estimating equations.
46.
:See System of linear equations for how to represent a collection of linear equations in the matrix vector form A "'x "'= "'b "'that is used in the description of the linear least squares method .-- Talk 09 : 29, 22 November 2006 ( UTC)
47.
When the problem has substantial uncertainties in the independent variable ( the " x " variable ), then simple regression and least squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares.
48.
A spreadsheet application of this for parabolic curves has been developed by NTS . The spreadsheet fits a parabola to 4 or more points ( up to 10 allowed ) using the least squares method and then calculates the limb length ( s ) using Simpson's Rule to evaluate the definite integral.
49.
In 1945 to 1965, Wold proposed and elaborated on his " recursive causal chain " model, which was more appropriate for many applications, according to Wold : For such " recursive causal chain " models, the least squares method was computationally efficient and enjoyed superior theoretical properties, which it lacked for general time-series models.
50.
In the next figure the break point is found at X = 7.9 while for the same data ( see blue figure above for mustard yield ), the least squares method yields a break point only at X = 4.9 . The latter value is lower, but the fit of the data beyond the break point is better.
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